Question

Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 247 with 146 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

90% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 146 / 247 = 0.591

1 - = 1 - 0.591 = 0.409

Z_/2 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.591 * 0.409) / 247)

= 0.051

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.591 - 0.051 < p < 0.591 + 0.051

0.540 < p < 0.642

90% C.I. = 0.540 , 0.642